Statistics,data analysis and Psychometrika: Major developments

Approximately 15% of all papers appearing inPsychometrika during the period 1960–1984 have been statistical or data analytic in nature. While these papers cover a very wide range of issues and are technically quite similar to those appearing in other major statistical journals, collectively they possess features which make them identifiablyPsychometrika.     

Models,computers and policies: Fifty years of Psychometrika

Mathematical models have been represented inPsychometrika first in biophysics, then in stochastic models of behavior, and later in computer simulations of behavior. Other specialized journals now attract many articles in these areas, butPsychometrika's policy of broad interest in all aspects of quantitative psychology remains sound. This paper reviewsPsychometrika's coverage of mathematical models and computation, and discusses some matters of editorial policy.     

Higher-order exploratory factor analysis of the Reynolds Intellectual Assessment Scales with a referred sample

The factor structure of the Reynolds Intellectual Assessment Scales (RIAS; [Reynolds, C.R., & Kamphaus, R.W. (2003). Reynolds Intellectual Assessment Scales. Lutz, FL: Psychological Assessment Resources, Inc.]) was investigated with a large (N = 1163) independent sample of referred students (ages 6-18). More rigorous factor extraction criteria (viz., Horn's parallel analysis (HPA); [Horn, J.L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30, 179-185.], and Minimum Average Partial (MAP) analysis; [Velicer, W.F. (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 41, 321-327.]), in addition to those used in RIAS development, were investigated. Exploratory factor analyses using both orthogonal and oblique rotations and higher-order exploratory factor analyses using the Schmid and Leiman [Schmid, J., and Leiman, J.M. (1957). The development of hierarchical factor solutions. Psychometrika, 22, 53-61.] procedure were conducted. All factor extraction criteria indicated extraction of only one factor. Oblique rotations resulted in different results than orthogonal rotations, and higher-order factor analysis indicated the largest amount of variance was accounted for by the general intelligence factor. The proposed three-factor solution was not supported. Implications for the use of the RIAS with similarly referred students are discussed.     

Scaling and Psychometrika: Spatial and alternative representations of similarity data

Progress over the past twenty-five years in the development and improvement of models for representation of similarity data is reviewed. The discussion includes comments on class, dimensional, ideal type, and dichotomous attribute representations of underlying similarity structures. Most of the theoretical research in the area appeared, and continues to appear, inPsychometrika.     

A loss function for alpha factor analysis

Most of the factor solutions can be got by minimizing a corresponding loss function. However, up to now, a loss function for the alpha factor analysis (AFA) has not been known. The present paper establishes such a loss function for the AFA. Some analogies to the maximum likelihood factor analysis are discussed.The author is greatly indebted to Prof. Henry F. Kaiser (University of California, Berkeley) for his kind encouragement. He is also indebted to an anonymous referee ofPsychometrika for having confronted him with the problem in 1977. Financial support by the Wiener Hochschuljubiläumsstiftung is gratefully acknowledged.     

A note on item analysis and the criterion of internal consistency

The implications contained in Richardson's article on item analysis in March 1936 issue ofPsychometrika are examined in the light of multiple factor theory. It is shown that item analysis is a necessary, but not a sufficient condition for the construction of a test which shall measure a single trait. The intercorrelations of certain items selected by a method of item analysis are examined, found to contain many zero and some negative correlations. Multiple factor analysis showed that eight traits were measured by the items which had been asserted to measure only one.     

Factor pattern of test items and tests as a function of the correlation coefficient: Content,difficulty, and constant error factors

A dilemma was created for factor analysts by Ferguson (Psychometrika, 1941,6, 323–329) when he demonstrated that test items or sub-tests of varying difficulty will yield a correlation matrix of rank greater than 1, even though the material from which the items or sub-tests are drawn is homogeneous, although homogeneity of such material had been defined operationally by factor analysts as having a correlation matrix of rank 1. This dilemma has been resolved as a case of ambiguity, which lay in (1) failure to specify whether homogeneity was to apply to content, difficulty, or both, and (2) failure to state explicitly the kind of correlation to be used in obtaining the matrix. It is demonstrated that (1) if the material but (2) if content is homogeneous but difficulty is not, the homogeneity of the content can be demonstrated only by using the tetrachoric correlation coefficient in deriving the matrix; and that the use of the phi-coefficient (Pearsonianr) will disclose only the nonhomogeneity of the difficulty and lead to a series ofconstant error factors as contrasted withcontent factors. Since varying difficulty of items (and possibly of sub-tests) is desirable as well as practically unavoidable, it is recommended that all factor analysis problems be carried out with tetrachoric correlations. While no one would want to obtain the constant error factors by factor analysis (difficulty being more easily obtained by counting passes), their importance for test construction is pointed out.     

Social support,coping, and depressive symptoms in cardiac illness among Hispanic and non-Hispanic White cardiac patients

In Multi-Trait Multi-Method (MTMM) studies of causal attributions for laboratory events, there is little evidence of convergent and discriminant validity for attribution measures. We report the first MTMM study to investigate the validity of two methods of eliciting causal beliefs for an illness, specifically, myocardial infarction. Adult respondents (N?=?107) listed causes of MI, then completed questionnaire rating scales for causal beliefs for MI. Measures were compared using both Campbell and Fiske's approach to MTMM analyses, and a Confirmatory Factor Analysis approach. Neither single item measures causal beliefs, nor scales of causal beliefs derived using exploratory factor analysis provided much evidence of convergent and discriminant validity. Confirmatory factor analysis showed that a model containing only causal belief factors provided a moderately good fit to the data. Adding a questionnaire method factor significantly improved the fit of the model, as well as substantially changing the pattern of factor loadings: loadings of questionnaire items on causal belief factors were markedly reduced. These results highlight major problems with the measurement of causal beliefs, and in particular question the validity of factor analysis of questionnaire measures of causal beliefs. They also suggest that at least some of the MI causal belief factors reported in the literature are artefacts of common questionnaire method variance.     

Structural modeling and psychometrika: An historical perspective on growth and achievements

The field of linear structural equation modeling with continuous variables is reviewed. Trends in psychometric theory and data analysis across the five decades of publication ofPsychometrika are discussed, especially the clarification of concepts of population and sample, explication of the parametric structure of models, delineation of concepts of exploratory and confirmatory data analysis, expansion of statistical theory in psychometrics, estimation via optimization of an explicit objective function, and implementation of general function minimization methods. Developments in the ideas of factor analysis, latent variables, as well as structural and causal modeling are noted. Some major conceptual achievements involving general covariance structure representations, multiple population models, and moment structures are reviewed. The major statistical achievements of normal theory generalized least squares estimation, elliptical and distribution-free estimation, and higher-moment estimation are discussed. Computer programs that implement some of the theoretical developments are described.This review was supported in part by USPHS grants DA00017 and DA01070.     

Exploratory factor analysis for small samples

Traditionally, two distinct approaches have been employed for exploratory factor analysis: maximum likelihood factor analysis and principal component analysis. A third alternative, called regularized exploratory factor analysis, was introduced recently in the psychometric literature. Small sample size is an important issue that has received considerable discussion in the factor analysis literature. However, little is known about the differential performance of these three approaches to exploratory factor analysis in a small sample size scenario. A simulation study and an empirical example demonstrate that regularized exploratory factor analysis may be recommended over the two traditional approaches, particularly when sample sizes are small (below 50) and the sample covariance matrix is near singular.     

Major Factors of Personality

Summary

French has recently resurveyed the literature regarding personality factors in order to (a) update his previous survey and (b) complement, in the noncognitive domain, the prestigious French, Ekstrom, and Price kit of reference tests for cognitive factors. This recent survey of personality factors is limited in at least two respects: (a) it relies on studies which are, in most cases, limited in size of item pools; (b) it has been greatly influenced by the two systems of Cattell and Guilford. Rather than rely on the pre-1971 literature (which belongs to an era when the factor analysis of a hundred variables was “a large factor analysis”), the writer has undertaken research aimed at accurate delineation of personality factors using itemfactoring coupled with item analysis. The article has two purposes: (a) to compare the factors in French's survey with those emerging in very recent work, and (b) to make the point that we are now likely to achieve greater comprehensiveness and accuracy in the identification of major personality factors.     

Psychology as a quantitative rational science (excerpts)

The purpose of the Psychometric Society is to encourage mathematical psychology. This article justifies the emphasis on quantification, and upon rationalization in science, as well as the Society's conception of the fundamental nature of science.Editor's Note: On September 4, 1936, L. L. Thurstone gave the presidential address at the first annual meeting of the Psychometric Society in Hanover, NH. Uncertainties about the viability of the new journal,Psychometrika, led his colleagues to urge him to publish his address inScience. Excerpts from that paper are reprinted here. Thurstone's examples are now quite dated, and have been omitted, thus thwarting his major intent of providing examples of quantification. But his point of view towards the goals of the new Society is remarkably fresh, and is expressed with typical Thurstone clarity. The reference to the complete paper is:Thurstone, L. L. (1937). Psychology as a quantitative rational science.Science, 85, 227–232. (Copyright 1937 by the American Association for the Advancement of Science.)     

Development and validation of the Indonesian Well‐being Scale

The present study describes the development and validation of a new instrument to measure the well‐being of Indonesian people. Items were generated by taking into account the recent cross‐cultural developments in the literature. Participants (N = 1,028) from a number of provinces in Indonesia completed an online or a paper questionnaire containing a battery of measures, including the new well‐being instrument. The total sample was randomly split into two equal groups. An exploratory factor analysis (n = 516) was conducted on one half to explore the factor structure of the new scale, which resulted in a 24‐item scale with a four‐factor solution. The four factors were (a) Basic Needs, (b) Social Relation, (c) Acceptance, and (d) Spirituality. A confirmatory factor analysis was conducted on the second half (n = 516), which confirmed the four‐factor structure with 20 items emerging as the best and most parsimonious fit of the data. The psychometric properties of the final scale were tested on the whole sample. The new scale displayed sound internal consistency, test‐retest reliability, and divergent, convergent, and discriminant validity. The scale has the potential to be used in future research which examines well‐being in the Indonesia context. Future directions and limitations of the study are discussed.     

Validation de la version française de l'échelle de réflexivité en groupe de Carter et West, 1998

Several studies found reflexivity —the extent to which team discuss objectives, strategies and processes and adapt them to changes— to be related to team efficacy. Two studies were conducted with 80 teams (320 participants) to validate French version of reflexivity scale. In study 1 exploratory factor analysis revealed 3 factors which partly confirms the 2 factor structure (task reflexivity and social reflexivity) expected from the original study (Carter and West, 1998). Two items of the original task reflexivity scale load on a third factor we named strategic reflexivity. The three factor structure was replicated in study 2 with confirmatory factor analysis. Criterion validity is proved by correlations between reflexivity and team performance. Task, social and strategic reflexivity correlate with different aspects of team effectiveness. The French version of reflexivity scale is reliable and appropriate for evaluating team reflexivity.     

Accommodation,prediction and replication: model selection in scale construction

In psychology, measurement instruments are constructed from scales, which are obtained on the grounds of exploratory and confirmatory factor analysis. Looking at the literature, one can find various recommendations regarding how these techniques should be used during the scale construction process. Some authors suggest to use exploratory factor analysis on the entire data set while others advice to perform an internal cross-validation by randomly splitting the data set in two and then either perform exploratory factor analysis on both parts or exploratory factor analysis on the first part and confirmatory factor analysis on the other. In spite of all these divergent recommendations, there is no consensus on which method yields the best result. In this paper, we analyze this issue in light of the prediction versus accommodation debate and argue that the answer to this question depends on one’s conception of the criteria that should be used to achieve the goals of the scientific enterprise.

     

Test theory and psychometrika: The past twenty-five years

On the occasion ofPsychometrika's fiftieth anniversary, the past twenty-five years' developments in mental test theory are reviewed, with special emphasis on the topics receiving attention in the pages of this journal. (Analogous reviews forPsychometrika's first quarter century were given by Gulliksen and Guilford in 1961.) Much of the recent progress in test theory (and in other branches of psychometrics as well) has been made by treating the problems in this field as being essentially ones of statistical inference. It is concluded that (a) research in test theory is in a healthy state and (b)Psychometrika is an important source of information about that research.     

Development of the Behavioral Evaluation of Disorders of Sleep Scale

We describe the development, preliminary psychometric properties, and cross-validation of the Behavioral Evaluation of Disorders of Sleep (BEDS: Schreck 1997/1998). Parental reports of problem sleep behavior in elementary school aged children 5 years to 12 years were collected for two samples. With the first sample, an exploratory factor analysis of parental responses (N = 307) resulted in reports of five distinct types of sleep problems: Expressive Sleep Disturbances; Sensitivity to the Environment; Disoriented Awakening; Sleep Facilitators; and Apnea/Bruxism. Four of these factors (Expressive Sleep Disturbances; Sensitivity to the Environment; Disoriented Awakening; and Apnea) were confirmed with the new participant sample (N = 1054). These factors of problem sleep behavior were similar to findings in other studies, with the exception of the exclusion of bedtime behavior problems.     

Exploratory factor analysis: its role in item analysis

The special characteristics of items-low reliability, confounds by minor, unwanted covariance, and the likelihood of a general factor-and better understanding of factor analysis means that the default procedure of many statistical packages (Little Jiffy) is no longer adequate for exploratory item factor analysis. It produces too many factors and precludes a general factor even when that means the factors extracted are nonreplicable. More appropriate procedures that reduce these problems are presented, along with how to select the sample, sample size required, and how to select items for scales. Proposed scales can be evaluated by their correlations with the factors; a new procedure for doing so eliminates the biased values produced by correlating them with either total or factor scores. The role of exploratory factor analysis relative to cluster analysis and confirmatory factor analysis is noted.     

Adaptation of a Muslim Spiritual Attachment Scale (God attachment) for Turkish Muslims: a validity and reliability study

ABSTRACT

Despite the importance of a believer’s attachment relationship with God for mental health, there are few measures relevant to Muslims, and little work on cross-cultural validation of such measures. The objective of the present study was to examine the validity and reliability of the Muslim Spiritual Attachment Scale (M-SAS) in Turkish Muslim samples. In analyzing the data, three different samples of college students (N?=?525, N?=?341, and N?=?47 respectively) were used. The validity and reliability of M-SAS were examined through exploratory factor analysis, confirmatory factor analysis, the internal consistency coefficient and the split-half reliability coefficient. Results supported a three-factor model of M-SAS with good reliability for the factors, and convergence with an alternative God Attachment measure. As a result, it may be concluded that M-SAS can be used as a valid and reliable measurement instrument in Turkish Muslim samples. The results are discussed in the light of the relevant literature.     

Evolution of Nonassociative Learning: Behavioral Analysis of a Phylogenetic Lesion

A recent phylogenetic analysis of two learning-related neuromodulatory traits in mechanosensory neurons of species related to the marine molluskAplysia californicaidentified one species,Dolabrifera dolabrifera,which lacked both neuromodulatory traits. Since these traits are thought to contribute importantly to certain forms of learning and memory in the defensive withdrawal reflexes ofAplysia,in the present study, I tested the prediction that facilitatory nonassociative learning would be reduced or absent inDolabrifera.I tested the tail-mantle withdrawal reflex inDolabriferaand size-matchedAplysiafor three forms of nonassociative learning and memory: dishabituation and short- and long-term sensitization. I found that the same protocols that produced significant dishabituation, short-term sensitization, and long-term sensitization inAplysiafailed in all three cases to produce significant learning inDolabrifera.Thus, the prediction from the prior mechanistic analysis is confirmed: Dishabituation and short- and long-term sensitization are significantly reduced and perhaps abolished inDolabrifera.Although not conclusive, this phylogenetic correlation between the absence of behavioral changes and the absence of neural mechanisms thought to underlie the behavioral changes gives support to the contemporary neuromodulatory model of dishabituation and sensitization inAplysia.Furthermore, these results raise the possibility that evolutionary alteration of two specific neuromodulatory mechanisms may have directly contributed to evolutionary change in behavioral plasticity.